\(S\)-convex, monotone, and positive interpolation with rational bicubic spline of \(C^ 2\)-continuity
The authors study certain bivariate rational cubic spline interpolants of the continuity class \(C^ 2\). Under certain conditions those splines are shape preserving, positive, monotone and preserve the so-called \(S\)- convexity of the data sets given on rectangular grids (the \(S\)-convexity implies the one-dimensional convexity in all directions with nonnegative ascent). To this end the authors propose and test a numerical search procedure.
scientific article; zbMATH DE number 503587
scientific article